Timeline for Are there oriented $4k+2$ manifolds such that $im(H_{2k+1}(M; Z/2)\to H_{2k+1}(M, \partial M; Z/2))$ has odd dimension?
Current License: CC BY-SA 2.5
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| Jan 30, 2011 at 15:58 | comment | added | Tom Goodwillie | Well, there's a nontrivial theorem of Thom, from his big 1954 paper on cobordism, to the effect that the canonical map from unoriented smooth bordism to mod 2 singular homology is surjective. (The analogue for oriented bordism and integral homology is false.) | |
| Jan 30, 2011 at 6:39 | comment | added | Greg Friedman | Tom is there a way to generalize this to cycles not represented by manifolds? | |
| Jan 29, 2011 at 4:38 | history | edited | Tom Goodwillie | CC BY-SA 2.5 |
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| Jan 29, 2011 at 1:11 | history | answered | Tom Goodwillie | CC BY-SA 2.5 |